The Idiographic Ising model release_rev_a93cc4f2-d694-4f97-88d8-88324907cdf9

Abstract

The Ising model is a graphical model that has played an essential role in the field of network psychometrics, where it has been used as a theoretical model to re-conceptualize psychometric concepts and as a statistical model for the analysis of psychological data. But in network psychometrics, the psychological data that are analyzed often come from cross-sectional applications, and the practice of using graphical models such as the Ising model to analyze these data has been heavily critiqued in the past few years. The primary voiced concern centers around the inability of the Ising model to express heterogeneity in the population, and the necessity to then assume that the population is homogeneous w.r.t. the network's structure in practice. But associations at the group-level may be entirely different from associations at the individual level, and it is unclear what the estimated relations from cross-sectional data imply for associations at the individual level. In this paper, an idiographic interpretation of the Ising model is developed that does not require that persons are exchangeable replications of a single topological structure. Working with a clear, formal connection between network relations at the individual- and the group level, we have unique topological structures that characterize individuals and aggregate into an Ising model cross-sectionally.
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